An analytical investigation and comparison of oscillating systems with nonlinear behavior using AGM and HPM

The purpose of this research is to use the Akbari Ganji Method, abbreviated as AGM, and the Homotopy Perturbation Method, abbreviated as HPM, to analytically investigate some oscillating systems with nonlinear behavior in a variety of situations and compare the results to the numerical approach to assess the validity and accuracy of these methods. Both of these cases were also stated in a circumstance in which one of the variables such as stiffness and length for instance, could also be changed to a finite number to demonstrate how these methods may be applied in various assumptions. The findings in all situations show the precision of both the AGM and HPM, with all computations showing an amazing similarity to the numerical method (c) 2022 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/ 4.0/).